Home Page of Dr. Myron Hlynka,

Queueing Theorist

Visit a collection of queueing theory material and pointers at Myron Hlynka's Queueing Theory Page.

Give an example of a word in the English language with five consecutive vowels.

The answer is QUEUEING!

Q: If you had a preemptive priority system with seven low priority customers in the system, and a high priority customer arrived and bumped the low priority customer from service, what name (from a Disney movie) would be appropriate to describe this situation?
A: No Wait and the Seven Dwarfs!

CanQueue 2012 Presentation:
http://web2.uwindsor.ca/math/hlynka/canqueue2012.pdf

CanQueue 2010 Presentation:
http://web2.uwindsor.ca/math/hlynka/HlynkaPostBeamerCanQ2010.pdf

CanQueue 2009 was held in Windsor, Ontario, Canada August 27-28, 2009. See
http://web2.uwindsor.ca/math/hlynka/canqueue2009.html

Dr. Myron Hlynka

Professional Accreditation and Memberships:

Research Interests

• Queueing Theory
• Applied Probability (This links to The Probability Web .)
• Stochastic Processes
• Operations Research. Two excellent resources are INFORMS OR/MS Resource Collection and the WORMS home page.
• Statistics (This links to the Statistics home page at the University of Florida.)

Graduate Students Supervised

1. Andrew LUONG, M.Sc.(Statistics), University of Alberta, 1983
   Master's Paper: Some Results in Reliability Using Death-Immigration and Renewal Processes
2. Wai-Hang POON, M.Sc.(Computer Science), University of Windsor, 1991, co-supervised with Dr. Henry Toews
   Master's Thesis: Dynamic Scheduling Strategies for Pseudo Parallel Queues: Observing Queues Before Joining
   http://scholar.uwindsor.ca/etd/1798/
3. Richard SCHELL, M.Sc. (Statistics), University of Windsor, 1994
   Master's Paper: A Queueing Model for Cholesterol
   (University of Windsor Gold Medalist - October, 1995)
4. Steve DREKIC, M.Sc. (Statistics), University of Windsor, 1995
   Master's Paper: Conditional Maximum Distributions and Random Truncation
   Currently a professor in the Dept of Statistics and Actuarial Sciences at the University of Waterloo.
5. Kirk ROY, M.Sc. (Statistics), University of Windsor, 1997.
   Master's Thesis: A Probabilistic Interpretation of Laplace Transforms
   - co-supervised with Dr. Richard Caron
   http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ31000.pdf
6. Mathew CHANDLER, M.Sc. (Statistics), University of Windsor, 1997.
   Master's Thesis: A Situational Analysis of the Sacrifice Bunt in Baseball
   http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ30937.pdf
7. Luat BUI, M.Sc. (Mathematics), University of Windsor, 1997.
   Master's Thesis: New Results in Partition Theory
   http://scholar.uwindsor.ca/etd/2848/
8. Todd BRAITHWAITE, M.Sc. (Statistics), University of Windsor, 1997.
   Master's Thesis: A Two Dimensional Bin Packing Algorithm.
   - co-supervised with Dr. Richard Caron
   http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ30932.pdf
9. Wayne HORN, M.Sc. (Statistics), 1999.
   Master's Thesis: Laplace Transforms of Order Statistics of Erlang Random Variables
   - co-supervised with Dr. Percy Brill.
   http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape10/PQDD_0014/MQ52571.pdf
10. Yingchun LUO M.Sc. (Statistics), 2000.
    Master's Major Paper: A Doubly Stochastic Inventory Model.
11. Matthew HAEHNEL. M.Sc. (Math), 2001.
    Master's Major Paper: A Modified Runs Test and the Stock Market.
12. Bashar ZOGHEIB. M.Sc. (Stat), 2002.
    Master's Major Paper: SAS and Approximations to the Standard Normal Cumulative Distribution Function.
13. Yong Xiang WU. M.Sc. (Stat), 2003.
    Master's Major Paper: M/M/c/c Queueing Systems and Parking Lots.
14. Huiling XIONG. M.Sc. (Stat), 2003.
    Master's Major Paper: Inequalities for a Parking Lot Queueing Model.
15. Yi Bei ZHANG. M.Sc. (Stat), 2004. (co-supervised with T. Traynor)
    Master's Major Paper: Convergence and Stochastic Stability of One Step Methods for Stochastic Differential Delay Equations.
16. Wen MIN. M.Sc. (Stat), 2005.
    Master's Major Paper: Exploratory Statistical Study of E-Bay Textbook Auctions.
17. Xiaoyong WU. Ph.D. (Stat), 2005. (co-supervised with P. Brill)
    Some Retrial Queueing Models.
18. Jing TANG. M. Sc. (Stat.) 2005. Control of Queues with Unknown Completion Time.
    http://web2.uwindsor.ca/math/hlynka/jingtangmajorpaper.pdf
19. Chinthanie RAMASUNDARAHETTIGE. M.Sc. (Stat). A Comparison of Several Queueing Software Packages. 2006.
    http://web2.uwindsor.ca/math/hlynka/ramamajorpaper.pdf
20. Dongfang CHANG. M.Sc. (Stat.) 2006.
    Major Paper: Queues which Form Prior to Opening of Service Facility.
21. Tolulope SAJOBI. M.Sc. (Stat.) Thesis. Markov Transition Matrices and Fibonacci Numbers (126 pp.) 2008. (Vanier Scholarship Winner)
22. Qianying WU. M.Sc. (Stat.) Major Paper: Some Properties of First Passage Distributions. 2008
23. Waqas ZUBERI. M.Sc. (Stat.) 2009.
    Major Paper: A Survey of Markov Applications to Medical Conditions. 2009.
24. Rifat JAHAN. M.Sc. (Stat.) 2009.
    Major Paper: Queueing Control and Laplace Transforms.
25. Shan XU. M.Sc. (Stat.) 2010.
    Major Paper: Some Results on Transient Queues.
26. Qian JIANG. M.Sc. (Stat.) 2011.
    Major Paper: Construction of Transition Matrices for Reversible Markov Chains
27. Mubeen HUSSAIN. M.Sc. (Stat.) 2011.
    Major Paper: Time to Ruin for Loss Reserves.
28. Chi Ho CHEUNG, PhD student. 2011-. In progress.
29. Qian JIANG, PhD student. 2011-. In progress.
30. Victoria CHERNOUKHOVA. M.Sc. student. 2012-. In progress.
31. Qianqian WANG. M.Sc. student, 2012-. In progress
32. Bingsen YAN. M.Sc. student., 2012-. In progress.

Undergraduate NSERC Summer Award Students Supervised

1. Wai-hang POON, 1989
2. Karen LUCIER Hill, 1990
~
3. Nicole LEMIRE, 1990, co-supervised with Dr. R. Caron
4. Kar WONG, 1992
5. Steve DREKIC, 1993
6. Kirk ROY, 1995, co-supervised with Dr. R. Caron
7. Jon CASEY, 2002.
8. Deborah LOACH, 2005, co-supervised with Dr. R. Caron
9. Laura HURAJT, 2006.
10. Anna CYLWA, 2007.
11. Michelle CYLWA, 2008.
12. Samantha MOLINARO, 2009.

Refereed Publications:

1. Hlynka, M. and Sheahan, J., 1986, Optimal Control Relating to the Excess of one Poisson Process over Another, Utilitas Mathematica, pp. 217-230.
   http://web2.uwindsor.ca/math/hlynka/utilitas217_230.PDF
2. Hlynka, M. and Sheahan, J., 1987, Controlling Rates for a Double Queue, Naval Logistics Research Quarterly, V. 34, pp. 569-577.
3. Hlynka, M. and Sheahan, J., 1988, The Secretary Problem for a Random Walk, Stochastic Applications and Their Applications, V. 28, pp. 317-325.
4. Hlynka, M., Sheahan, J. and Wiens, D.P, 1990, On the Choice of Support of Re-Descending Psi-Functions in Linear Models with Asymmetric Error Distributions, Metrika, V. 37, pp. 365-381.
5. Caron, R.J., Hlynka, M. and McDonald, J.F., 1992, On the Best Case Performance of Hit and Run Methods for Detecting Necessary Constraints, Mathematical Programming V. 54. pp. 233-249.
6. Khasnabish, B., Ahmadi, M., Hlynka, M. and Shridhar, M., 1993, Trading Nodal Storage Capacity with Incremental Transmission Capacity IEEE Transactions on Communications. Vol. 41, pp. 1147-1150.
7. Khasnabish, B., Ahmadi, M., Hlynka, M. and Shridhar, M., 1993, Trading Nodal Storage Capacity with Incremental Transmission Capacity in Supra-high-speed Packet-switching Nets, Canadian Journal of Electrical and Computer Engineering, Vol. 18, pp. 71-80.
8. Hlynka, M. and Wang, T., 1993. Comments on Duality of Queues with Finite Buffer Size, Operations Research Letters, V. 14, pp. 29-33.
9. Hlynka, M., Stanford, D., Poon, W. and Wang, T., 1994. Observing Queues before Joining, Operations Research, V. 42, pp. 365-342.
   http://www.jstor.org/action/showBasicSearch
10. Khasnabish, B., Ahmadi, M., Hlynka, M., and Shridhar, M. 1994. Design and Evaluation of a Smart Congestion -Level Indicator for a Large Group of Queues in ATM Networks, Proceedings of 1994 IEEE GLOBECOM, (refereed) V. 1, pp. 156-161.
11. Stanford, D. and Hlynka, M., 1996. Observing General Service Queues Before Joining, Operations Research Letters, V. 18, pp. 237-245.
12. M. Hlynka, S. Drekic and G. McPhail, 1997, A Non- Monotone Waiting Time Queueing Model, Utilitas Mathematica, 52, 83-89.
    http://web2.uwindsor.ca/math/hlynka/utilitas1997_83-89.PDF
13. P.H. Brill and M. Hlynka, 1998, A Single Server N-Line Queue in which a Customer May Receive Special Treatment, Stochastic Models. 14, 905-931.
14. P.H. Brill and M. Hlynka, 2000. "An Exponential Queue with Competition for Service," European Journal Of Operational Research (126)3 (2000) pp. 587-602.
15. J.C. Fedoruk, D. Paterson, M. Hlynka, K.Y. Fung, M. Gobet, W. Currie, 2002. "Rapid On-Site Defibrillation versus Community Program." Prehospital and Disaster Medicine, V. 17:2, pp. 102-106.
    http://pdm.medicine.wisc.edu/17-2pdf/102-106Fedoruk.pdf
16. M. Hlynka and L. Mandziuk. 2002. A Queueing Model for Attention- Deficit / Hyperactivity Disorder. Proceedings of SCI 2002, The 6th World Multi-Conference on SYSTEMICS, CYBERNETICS AND INFORMATICS. Orlando, Florida. July 14-16, 2002, Volume IV, 243-248.
    http://web2.uwindsor.ca/math/hlynka/orlando.pdf
17. P. Brill and M. Hlynka, 2002. A Geometric Interpretation of 2x2 Markov Transition Matrices. Missouri Journal of Mathematical Sciences. Volume 14, 2002. 159-174.
    http://www.math-cs.ucmo.edu/~mjms/2002.3/brill.pdf
18. M. Mandelbaum and M. Hlynka, 2003. Job Sequencing Using An Expert. International Journal of Production Economics, 85, 389-401.
19. M. Hlynka and M. Mandelbaum, 2003. Improving Computer Processing Efficiency by Sequencing. Chapter 33, of monograph High Performance Computing Systems and Applications, Kluwer Publishers, edited by Robert Kent and Todd Sands, pp. 313-327. Proceedings of the 2001 15th Annual Symposium on High Performance Computing Systems and Applications.
20. X. Wu, M. Hlynka, P. Brill, J. Wang. 2005. "An M/G/1 Retrial Queue with Balking and Retrials during Service." IJOR (International Journal of Operational Research), V. 1, 30-51.
21. M. Mandelbaum, M. Hlynka, P. Brill. 2007. "Nonhomogeneous Geometric Distributions with Relations to Birth and Death Processes." TOP (Journal of the Spanish Society of Statistics and Operations Research). Volume 15, pp. 281-296.
    If your university has access to Springer publications, you can view a copy at
    http://www.springerlink.com/content/a6303772r58x0722/
22. M. Hlynka and T. Sajobi. 2008. "A Markov Chain Fibonacci Model." Missouri Journal of Mathematical Sciences. Volume 20. No. 3. pp. 186-199.
    http://web2.uwindsor.ca/math/hlynka/hlynkasajobiams.pdf
23. M. Hlynka, W. Horn, R.Schell. 2008.
    Branching Processes with a Common Extinction Probability.
    International Journal of Pure and Applied Mathematics. V. 45, No. 2, 175-185.
    http://web2.uwindsor.ca/math/hlynka/ijpam175_185.PDF
24. C.K. Cavas, L. Cavas, M.B. Yokes, M. Hlynka, R. Schell, and K. Yurdakoc
    2008. A Novel Application of Queueing Theory on the Caulerpenyne Secreted by Invasive Caulerpa taxifolia (Vahl) C.Agardh (Ulvophyceae, Caulerpales): A Preliminary Study.
    Mediterranean Marine Science, VOLUME 9, NUMBER 1, JUNE 2008. pp. 67-75
    http://web2.uwindsor.ca/math/hlynka/mediterranean2008.pdf
25. M. Mandelbaum and M. Hlynka (2008) Examples of Applications of Queueing Theory in Canada. INFOR, 46(4) 29-46.
    http://web2.uwindsor.ca/math/hlynka/2008infor29_46.pdf
26. M. Hlynka, L. Hurajt, M. Cylwa. 2009. Transient Results for M/M/1/c Queues via Path Counting.
    International Journal of Mathematics in Operational Research. Volume 1, 2009, 20-36.
    http://web2.uwindsor.ca/math/hlynka/ijmor2009.pdf
27. P.H. Brill, M.L. Huang, M.Hlynka. 2009. Note on an Inventory System with Decay. IAENG International Journal of Applied Mathematics, Volume 39 Issue 3, 171-174.
    http://www.iaeng.org/IJAM/issues_v39/issue_3/IJAM_39_3_05.pdf
28. M. Hlynka, P.H. Brill, W. Horn. 2010. A Laplace Transform Method for Order Statistics of Erlang Random Variables. Probability and Statistics Letters. V. 80, 9-18.
    http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1D-4XBX70J-1&_user=1010624&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050266&_version=1&_urlVersion=0&_userid=1010624&md5=f3f8aad0e3eb0b3bf62b7e851d36ae93
29. Jerome Cohen, Xue Han, Anca Matei, Vara Parameswaran, Robert Zuniga, Myron Hlynka. 2010. Rats' Visual-Spatial Working Memory: New Object Choice Accuracy as a Function of Number of Objects in the Study Array. Learning and Motivation, v 41 pp. 125-140.
30. Marvin Mandelbaum and Myron Hlynka. 2009. A History of Queueing in Canada before 1980. INFOR. 47, pp. 335-353.
    http://www.docstoc.com/docs/68731872/History-of-Queueing-Theory-in-Canada-Prior-to-1980
31. Hlynka, M. 2011. The M/M/1 Queue. Wiley Encyclopedia of Operations Research and Management Science.
    http://onlinelibrary.wiley.com/doi/10.1002/9780470400531.eorms0891/full
32. Percy H. Brill, Myron Hlynka. 2012. Server Workload in an M/M/1 Queue with Bulk Arrivals and Special Delays. Applied Mathematics, 2012, 3, 2174-2177. Vol.3 No.12A
    http://www.scirp.org/journal/am

List of Technical Reports:

1. Hlynka, M. and Sheahan, J., 1987, Optimal strategies and Poisson Distribution, Technical Report, 4 pp.
2. Caron, R.J., Hlynka, M., and McDonald, J.F., 1988, Minimizing the Expected Number of Trials in the Coupon Collector's Problem, Windsor Mathematics Report 88-03, 5 pp.
3. Hlynka, M., 1988, Perishable Inventory Units with an Assignment Time, Windsor Mathematics Report #88-06, (Technical Report), 46 pp.
4. Hlynka, M. 1988 A Discrete Analog to the Method of Stages, Windsor Mathematics Report #88-11, 17 pp.
5. Hlynka, M., Sheahan, J.N., and Wiens,D.P, 1989, On Deleting Influential Responses Under a Model of Asymmetric Errors in Regression, University of Alberta Technical Report #89-25, 6 pp.
6. Hlynka, M. and Poon, W.H., 1989, A Computer Program for Parallel Queues, Windsor Mathematics Report #89-11 (Technical Report) 18 pp.
7. Hlynka, M. and Poon, W.H., 1989, Properties of the Steady State Probabilities of Two Parallel Queues, Windsor Mathematics Report #89-12, (revised July, 1990), 14 pp.
8. M. Hlynka and Wang, T., 1990, Comments on Duality of Queues with Finite Buffer Size, Windsor Mathematics Report #90-04, 14 pp.
9. Wang, T. and Hlynka, M., 1990, Two Parallel Queues with Partial Jockeying, Windsor Mathematics Report, #90-06, 15 pp.
10. Hlynka, M., Poon, W.H., and Wang, T., 1990, Observing Queues before Joining, Windsor Mathematics Report #90-07, 24 pp.
11. A.Atmani, R.Caron, M. Hlynka, R.Lashkari, and N. Lemire, 1992, School Bus Scheduling, A Preliminary Report. Windsor Mathematics Report #92-04, 61 pp.
12. M. Hlynka and C.K. Wong, 1993, An Improved Queue Joining Strategy, Windsor Mathematics Report #93-01, 10 pp.
13. S.V. Majety, M. Hlynka, and R.S. Lashkari, 1993, Determining the Number of AGV's in Assembly Line Processes.
14. P.H. Brill and M. Hlynka, 1993, The "Who's Next" Queue with Two Lines, Windsor Mathematics Report, 93-08, 21 pp.
15. D.A. Stanford and M. Hlynka, 1993, Observing General Service Queues Before Joining, 16 pp.
16. P.H. Brill and M. Hlynka, 1994, A Single Server N-Line Queue in which a Customer May Receive Special Treatment, Windsor Mathematics Report, 94-03, 21 pp.
17. M. Hlynka, S. Drekic and G. McPhail, 1994, A Non- Monotone Waiting Time Queueing Model, Windsor Mathematics and Statistics Report 94-05, 10 pp.
18. L. Mandziuk and M. Hlynka, 1995, A Queueing Model for Attention-Deficit / Hyperactivity Disorder, Windsor Mathematics and Statistics Report 95-02, 18 pp.
19. M. Hlynka, 1995, Statistical Distributions Arising in Perishable Inventory, Windsor Mathematics and Statistics Report 95-03, 12 pp.
20. K. Roy and M. Hlynka, 1995, Queueing in APL, Windsor Mathematics and Statistics Report 95-04, 13 pp.
21. J. Henderson and M. Hlynka, 1995, Risk Aversion and the Selection of a Target for Quality, Windsor Mathematics and Statistics Report 95-05, 11 pp.,
22. R.J. Caron, M. Hlynka, and K. Roy, 1995, Warranty Expense Forecasting using Operations Research, Report to Chrysler Canada Ltd., Windsor, Ontario. 22 pp. (Propietary)
23. K. Roy and M. Hlynka, 1995, Queueing Theory Applied to a Traffic Light Problem, Windsor Mathematics and Statistics Report #95-14, 18 pp.
24. M. Hlynka, 1995, Book Review of "Weighted Approximations in Probability and Statistics", by M. Csorgo and L. Lajos. Interfaces, Sept.-Oct., 1995, pp. 213-214.
25. P. Brill and M. Hlynka, 1997, "A Geometric Interpretation of Markov Transition Matrices", Windsor Math and Statistics Report, #97-01, 10 pp.
26. P. Brill and M. Hlynka, 1997, A Multiple Server "Who's Next?" Queue, Windsor Math and Statistics Report, #97-03, 14 pp.
27. P. Brill and M. Hlynka, 1997, Companion Results to L = lambda W, Windsor Math and Statistics Report, #98-01, 6 pp.
28. M. Hlynka, W. Horn, R. Schell, 1999. Branching Processes and Fibonacci Numbers. Windsor Math and Statistics Report, #99-02, 9 pp.
29. K. Roy, M. Hlynka. and R. Caron, 1999. Laplace Transform for the Busy Period of an M/G/1 System, Windsor Math and Statistics Report, #99-05, 7 pp.
30. J. Casey and M. Hlynka. 2002. The Parrondo Paradox and Queueing. Windsor Math and Statistics Report, #02-02, 13 pp.
31. M. Hlynka and D. Loach. 2005. Generating Uniform Random Points in a Regular $n$ Sided Polygon. WMSR #05-02. 8 pp.
    http://web2.uwindsor.ca/math/hlynka/Ngon.pdf
32. M. Hlynka. 2006. Introduction to the Statistical Language R. WMSR #06-04. Revised 2008.
    http://web2.uwindsor.ca/math/hlynka/HlynkaIntroToR.pdf
33. M. Hlynka. 2007. Some Examples of Graphics in the Statistical Language R. June 13, 2007.
    http://web2.uwindsor.ca/math/hlynka/RgraphicsHlynka.pdf
34. M. Mandelbaum, M. Hlynka and P.H. Brill, 2006. Nonhomogeneous Geometric Distribution Representations and Queueing. WMSR #06-03.
    (appeared in TOP: Spanish Operational Research Society Journal Volume 15, 2007, pp. 281-296.)
35. M. Hlynka and L.M. Hurajt. 2006. "M/M/1 Transient Queues and Path Counting." WMSR #06-05.
    http://web2.uwindsor.ca/math/hlynka/hlynkahurajt.pdf
36. M. Hlynka and P.H. Brill. 2007. Stability in M/M/1 Queues with Reneging. WMSR #07-09
37. M. Hlynka and P.H. Brill. 2008. "A Result for a Counter Problem." WMSR #08-01.
38. M. Hlynka and M. Cylwa. 2009.
    Observations on the Metropolis-Hastings Algorithm." WMSR #09-06.
39. M. Hlynka and S. Molinaro. 2009.
    "Calculating Transient Probabilities of an M/M/1 Queue: R program and Test Bank." WMSR #09-07.
40. S. Molinaro and M. Hlynka. 2009.
    Comparing System Times In An Unordered Two Queue network.
    WMSR #09-08.
41. B. Zogheib and M. Hlynka. 2009.
    Approximations of the Standard Normal Distribution. WMSR #09-09.
42. S. Molinaro, M. Hlynka, S. Xu. 2011
    Two Unordered Queues. ArXiv 1108.1179, 17 pp. WMSR #11.03

Manuals

• M. Hlynka, Statistical Packages at the University of Alberta, 1983, 153 pp.
• M. Hlynka, A Brief Introduction to Queueing Theory, 1994, 61 pp.

Other Activities:

• Member of the organizational committee for the ORSA/TIMS Annual Meeting in Detroit in October, 1994.
• Member of the organizational committee for the Canadian Operations Research Society (CORS) National Convention in Windsor in 1999.
• Member of the organizing committee for the 16th International Workshop on Matrices and Statistics. 2007. Windsor, Ontario.
• local organizer from the Putnam Mathematical Competition at the University of Windsor since 1986. In the earlier years, this was done jointly with Dr. Michael Selby. After Michael retired, this was done by MH alone until 2006, after which the Putnam was locally organized jointly by MH and Dr. Wai Ling Yee.
• Chief organizer of CanQueue 2009 (Canadian Queueing Conference) in Windsor, August, 2009.
• Local administrator of the SOA Actuarial Exams, since 2002.
• Arranged annual visits, from 1995-2012, by Towers Watson/ Watson Wyatt Company personnel to U of W to discuss actuarial careers.

Other Neat Links

• For an interesting set of articles and biographies on the history of mathematics housed at the University of St. Andrews in Scotland, click on Math History.
• Mathematical Geneology (Who was your advisor's advisor?)
  http://www.genealogy.ams.org/
• Are there any males out there who have wondered about tying their ties when they dress up in a suit? See
  http://www.tcm.phy.cam.ac.uk/~ym101/tie/aps97tie.html
• For an entertaining online magazine about mathematics, from Cambridge University, visit
  http://plus.maths.org/
  If you enjoy this kind of mathematics, we would enjoy having you as a student at the University of Windsor.

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  Visit Myron Hlynka's math Tricks for Science Rendezvous 2012 at
  http://web2.uwindsor.ca/math/hlynka/mathtricks.html